| Exam Board | WJEC |
|---|---|
| Module | Further Unit 2 (Further Unit 2) |
| Year | 2019 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | Apply E(aX+b) or Var(aX+b) formulas directly |
| Difficulty | Challenging +1.2 This question requires understanding that X and Y are binomial distributions, applying E(XY) = E(X)E(Y) for independent variables, and using the variance formula Var(XY) = E(X²)E(Y²) - [E(X)E(Y)]². While it goes beyond direct application of E(aX+b) formulas and requires knowledge of product moments for independent variables, these are standard Further Maths techniques with straightforward algebraic manipulation once the correct formulas are recalled. |
| Spec | 5.04a Linear combinations: E(aX+bY), Var(aX+bY) |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | Jan-Mar | 259 |
Question 2:
2 | Jan-Mar | 259 | 217.252. The probability of winning a certain game at a funfair is $p$. Aman plays the game 5 times and Boaz plays the game 8 times. The independent random variables $X$ and $Y$ denote the number of wins for Aman and Boaz respectively.
\begin{enumerate}[label=(\alph*)]
\item Given that $\mathrm { E } ( X Y ) = 6 \cdot 4$, calculate $p$.
\item Find $\operatorname { Var } ( X Y )$.
\end{enumerate}
\hfill \mbox{\textit{WJEC Further Unit 2 2019 Q2 [9]}}